Related papers: Data-based prediction and causality inference of n…

We introduce and test a general machine-learning-based technique for the inference of short term causal dependence between state variables of an unknown dynamical system from time series measurements of its state variables. Our technique…

Reconstructing the equation of motion and thus the network topology of a system from time series is a very important problem. Although many powerful methods have been developed, it remains a great challenge to deal with systems in high…

Recent work has focused on data-driven learning of the evolution of unknown systems via deep neural networks (DNNs), with the goal of conducting long term prediction of the dynamics of the unknown system. In many real-world applications,…

We present a nonparametric way to retrieve a system of differential equations in embedding space from a single time series. These equations can be treated with dynamical systems theory and allow for long term predictions. We demonstrate the…

The machine learning community has recently devoted much attention to the problem of inferring causal relationships from statistical data. Most of this work has focused on uncovering connections among scalar random variables. We generalize…

Time series are all around in real-world applications. However, unexpected accidents for example broken sensors or missing of the signals will cause missing values in time series, making the data hard to be utilized. It then does harm to…

We propose an approach for learning the causal structure in stochastic dynamical systems with a $1$-step functional dependency in the presence of latent variables. We propose an information-theoretic approach that allows us to recover the…

Data-driven models for predicting dynamic responses of linear and nonlinear systems are of great importance due to their wide application from probabilistic analysis to inverse problems such as system identification and damage diagnosis. In…

We study the problem of modeling a non-linear dynamical system when given a time series by deriving equations directly from the data. Despite the fact that time series data are given as input, models for dynamics and estimation algorithms…

This work aims to improve generalization and interpretability of dynamical systems by recovering the underlying lower-dimensional latent states and their time evolutions. Previous work on disentangled representation learning within the…

This paper reports on the application to field measurements of time series methods developed on the basis of the theory of deterministic chaos. The major difficulties are pointed out that arise when the data cannot be assumed to be purely…

The identification of a nonlinear dynamic model is an open topic in control theory, especially from sparse input-output measurements. A fundamental challenge of this problem is that very few to zero prior knowledge is available on both the…

We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by…

Novel method of reconstructing dynamical networks from empirically measured time series is proposed. By examining the variable--derivative correlation of network node pairs, we derive a simple equation that directly yields the adjacency…

Causal relationships play a fundamental role in understanding the world around us. The ability to identify and understand cause-effect relationships is critical to making informed decisions, predicting outcomes, and developing effective…

With the advancement of data science, the collection of increasingly complex datasets has become commonplace. In such datasets, the data dimension can be extremely high, and the underlying data generation process can be unknown and highly…

We present a numerical framework for recovering unknown non-autonomous dynamical systems with time-dependent inputs. To circumvent the difficulty presented by the non-autonomous nature of the system, our method transforms the solution state…

Many engineered as well as naturally occurring dynamical systems do not have an accurate mathematical model to describe their dynamic behavior. However, in many applications, it is possible to probe the system with external inputs and…

To understand, predict, and control complex networked systems, a prerequisite is to reconstruct the network structure from observable data. Despite recent progress in network reconstruction, binary-state dynamics that are ubiquitous in…

The paper introduces a novel topological method for prediction and modeling for a nonlinear time--series that exhibit recurring patterns. According to the model, global manifold of the reconstructed state--space can be approximated by a few…